6.
Ahmad claims that the difference of squares method of factoring can be used even when the values aren't perfect squares. An example of his thinking is shown.

6.Ahmad Claims That The Difference Of Squares Method Of Factoring Can Be Used Even When The Values Aren't

Answers

Answer 1

Answer:

Below.

Step-by-step explanation:

a. (x - √5)(x + √5)

= x(x + √5) - √5(x + √5)

= x^2 + √5x - √5x - 5

= x^2 - 5.

b. 10 - 3x^2

= (√10 - √3x) (√10 + √3x)

Answer 2

(a) Ahmad's factorization is correct.

(b)  (√10 - √3x)(√10 + √3x)

Given equation as

x² - 5 = (x - √5)(x + √5)

What is a Perfect Square?

A Perfect Square is defined as when multiplying an integer by itself, we get a perfect square, which is a positive integer. In simple words, we can say that perfect squares are numbers that are the products of integers by themselves.

Solution of (a)

Taking RHS from the given equation

⇒ (x - √5)(x + √5)

⇒ x(x + √5) - √5(x + √5)

⇒ x² + √5x - √5x - 5

⇒ x² - 5.

So, RHS = LHS

Hence, Ahmad's factorization is correct.

Solution of (b)

⇒ 10 - 3x²

According to Ahmad's strategy  

⇒ √10(√10 + √3x) - √3x(√10 + √3x)

(√10 - √3x)(√10 + √3x)

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Related Questions

find the measure of the indicated angle to the nearest degree​

Answers

[tex]\boxed{\sf sin\theta=\dfrac{P}{H}}[/tex]

[tex]\\ \sf\longmapsto sin\theta=\dfrac{38}{53}[/tex]

[tex]\\ \sf\longmapsto sin\theta=0.7[/tex]

[tex]\\ \sf\longmapsto sin\theta=\dfrac{1}{1.4}[/tex]

[tex]\\ \sf\longmapsto sin\theta=\dfrac{1}{\sqrt{2}}[/tex]

[tex]\\ \sf\longmapsto sin\theta=sin45°[/tex]

[tex]\\ \sf\longmapsto \theta=45°[/tex]

On a coordinate plane, a curved line with a minimum value of (1.5, negative 1) and a maximum value of (negative 1.5, 13), crosses the x-axis at (negative 3, 0), (1, 0), and (2, 0), and crosses the y-axis at (0, 6).
Which lists all of the x-intercepts of the graphed function?

(0, 6)
(1, 0) and (2, 0)
(1, 0), (2, 0), and (–3, 0)
(1, 0), (2, 0), (–3, 0), and (0, 6)

Answers

Answer:

Third option: (1, 0), (2, 0), and (–3, 0)

Step-by-step explanation:

The x-intercepts are the points at which the graph of the function crosses the x-axis.

By reading the question, we can see that:

"... crosses the x-axis at (negative 3, 0), (1, 0), and (2, 0)..."

So the x-intercepts are:

(-3, 0)

(1, 0)

(2,  0)

Then the correct option is the third one:

"(1, 0), (2, 0), and (–3, 0)"

Answer: Option 3

Step-by-step explanation: Got it right on Edge

using the graph, determine the coordinates of the roots of the parabola​

Answers

Answer:

(-8, 0) and (-2, 0)

Step-by-step explanation:

The root of a parabola are the places at which the parabola intersects the x-axis. As one can see, on the graph these points are the following: (-8, 0) and (-2, 0). Thus, the roots of the parabola are (-8, 0) and (-2, 0).

Answer:

-8 and -2

Step-by-step explanation:

Hello!

The roots of the parabola are the points where the graph intersects the x-axis. The x-axis is the equation y = 0.

There are two roots for this parabola, as the vertex is lower than y=0, and it opens up.

The two points of intersection are:

(-8,0)(-2,0)

Therefore, the roots of the parabola are -8 and -2.


Times for an ambulance to respond to a medical emergency in a certain town are normally distributed with a
mean of 450 seconds and a standard deviation of 50 seconds.
Suppose there are 97 emergencies in that town.
In about how many emergencies are the response times expected between 400 seconds and 500 seconds?
31
33
47
66

Answers

Answer:

66

Step-by-step explanation:

The Empirical Rule states that 68% of data is between 1 standard deviation in a dataset of normal distribution, 95% falls between 2 standard deviations, and 99.7% between 3.

The mean is 450, and one standard deviation is between 450 ± 50 = 400 and 500. Therefore, we can say that 68% of the data falls between 400 and 500 seconds.

The data includes 97 emergencies, so we just need to find 68% of that, which is 0.68*97 = 65.96 (rounding up to 66)

There are 66 emergencies are the response times expected between 400 seconds and 500 seconds.

What is Addition?

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

mean = 450 sec

standard deviation = 50 sec

Hence, We get;

450-50 =400

450+50=500

Now, In Between 400 sec and 500 sec means one deviation above and one deviation below the mean, and it is 68%.

68% = 0.68

Thus,

0.68 x 97 = 65.96 ≈ 66

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m% of a number equals n. can you find the number?

Answers

Answer:

mn/100

Step-by-step explanation:

m/100 * n = number = mn/100

Assuming m and n are variables with no values.

Suppose you invest $2200 at an annual interest rate of 5.3% compounded continuously. How much will you have in the account after 7 years?

Type your answers and then click Done.

What is the value of P?


Fill in the blank text field 1


What is the value of r in decimal form?

Fill in the blank text field 2


What is the value of t?

Answers

Answer:

2200, 0.053 and t=7

Step-by-step explanation:

Intrest will be 3158. 1

Help with step by step solution please

Answers

Answer:

5/2

Step-by-step explanation:

The square root of 5 divided by the negative square root of 5 equals -1. 7/2 - 1 = 5/2.

A rectangular drawing is enlarged by 30%. The original dimensions of this drawing are 16cm x 24cm.
Determine the scale factor, as a fraction that represents this enlargement. What are the new, enlarged
dimensions?

Answers

Answer:

Step-by-step explanation: Scale [tex]\frac{130}{100} = \frac{13}{10}[/tex]

New dimensions [tex]16 * 1.3 --- 24*1.3 =20.8 cm * 31.2 cm[/tex]

You are testing the claim that the proportion of men who own cats is larger than the proportion of women who own cats. You sample 170 men, and 70% own cats. You sample 190 women, and 40% own cats. Find the proportion of the pooled samples, ( p c pc ), as a decimal, rounded to two decimal places.

Answers

Answer:

The proportion of the pooled samples is 0.54.

Step-by-step explanation:

We have that:

70% of men own cats.

The proportion of men in the sample is:

[tex]\frac{170}{170+190} = 0.4722[/tex]

40% of women own cats.

The proportion of women in the sample is: 1 - 0.4722 = 0.5278

Proportion of the pooled samples

[tex]p = 0.7*0.4722 + 0.4*0.5278 = 0.54[/tex]

The proportion of the pooled samples is 0.54.

câu nào không phải mệnh đề
A. 3+2=7
B. 4+x

Answers

Answer:

b because it is an expressio n

Step-by-step explanation:

Using Eulers formula, how many edges does a polyhedron with 6 faces and 6 vertices have? Eulers Formula: F+V=E+2

Answers

Answer:

10

Step-by-step explanation:

E = F + V - 2

E = edges

F = faces = 6

V = vertices = 6

E = 6 + 6 - 2

E = 12 -2

E = 10

Which of the following sets represent D ∪ E?
{2, 4, 5, 6, 8, 15}
{2, 4, 5, 6, 8, 10, 15, 20}
{10, 20}
{3, 7, 9, 11}

Answers

Answer:

{2,4,5,6,8,10,15,20}

Answer:

{ 2,4,5,6,8,10,15,20}

Step-by-step explanation:

D ∪ E

This means the union of the two sets or what is in both circles with no duplicates

{ 2,4,5,6,8,10,15,20}

How do you make x the subject of the formula?
I need help on this one
y= 7x-1​

Answers

Answer:

x=[tex]\frac{y+1}{7}[/tex]

Step-by-step explanation:

Hi there!

We want to make x the subject of the formula, which means to solve the formula for x

Here is the given formula:

y=7x-1

Our ultimate goal is to isolate x onto one side

Start by subtracting 7x from both sides

y-7x=-1

Subtract y from both sides to remove it from the left side

-7x=-y-1

Divide both sides by 7

x=[tex]\frac{-y-1}{-7}[/tex]

Simplify (factor -1 out of the numerator and denominator, then cancel it out)

x=[tex]\frac{-1(y+1)}{(-1)(7)}[/tex]

x=[tex]\frac{y+1}{7}[/tex]

Hope this helps!

Answer:

x = 1/7(y+1)

or

x = 1/7 y + 1/7

Step-by-step explanation:

y= 7x-1​

Solve for x

Add 1 to each side

y+1 = 7x-1+1

y+1 = 7x

Divide each side by 7

1/7(y+1) = 7x/7

1/7y + 1/7 =x

Square inscribed in a circle with radius 16.

I’ll mark u as a brainliest!!

Answers

Answer:

if your trying to find the area of the square it's 1024 if your trying to find the circumference of the circle it's 32π ( also known as 32 x pi)

determine the general term of this sequence -15:-11;-7;,,173

Answers

Answer:

UWUNOE BRO HUUZEM HIHUDHS

Step-by-step explanation:

When Jonathan runs the 400 meter dash, his finishing times are normally distributed with a mean of 88 seconds and a standard deviation of 2.5 seconds. If Jonathan were to run 48 practice trials of the 400 meter dash, how many of those trials would be between 89 and 91 seconds, to the nearest whole number?

Answers

Answer:

3.18%

2 between 89   91

Step-by-step explanation:

*Probability-Between 3.18%

Z1=0.04 Z2=0.12

x-1 89

x-2 (not required) 91

µ 88

σ 25

eexpres -25/60 as a rational number whose denominator is -12​

Answers

Answer: 5/-12

Explanation

Divide both the denominator and the numerator by -5 to obtain the denominator of -12 and the numerator of 5.

5/-12

Hope this helps :)

Geometry edulastic question

Answers

9514 1404 393

Answer:

  n = 16

Step-by-step explanation:

Angle ABC is the sum of its parts.

  ∠ABC = ∠ABF +∠FBC

  159° = (7n +20)° +(2n -5)°

  159° = 9n° +15° . . . . . . . . . . . . . . collect terms

  144° = 9n° . . . . . . . . . . subtract 15°

  16° = n°

  n = 16

I need help plz anyone I don't understand this at all.

Answers

Answer:

jejejjejejr

Step-by-step explanation:

uejejjejejjsjs

1/4x-2= -6+ 5/12x1/4x-5/12x= -6+23x-5x/12 = -43x-5x= -4×122x= -48x= -48/2x= -24

Need answers please

Answers

Answer:

C

Step-by-step explanation:

you are adding

-3√18=

-27

√16=4

-27+4=-23

- 5x + x - 6x²
6x3 - 4 - 5 + 6x3 - 3x3

Answers

Is this all one equation?

If it isn't, here:

-6x ^ 2 - 4x <-- Equation 1

18 - 9 + 18 - 9 = 18 <-- Equation 2

If it is:

-5x + x - 6x ^ 2 + 6 * 3 - 4 - 5 + 18 - 9

-4x - 6x ^ 2 + 18 - 9 + 18 - 9

-4x - 6x ^ 2 + 18

Then we order it

-6x ^ 2 - 4x + 18

What is the value of a in the function equation?

Answers

Answer:

c

Step-by-step explanation:

cho hình thang vuông abcd vuông tại A và D có AD= a căn 3, DC=3,AB= 2a. chứng minh AC vuông góc với BD

Answers

I am not understanding the language

Answer:

its Vietnamese

Step-by-step explanation:

I just dont understand what that type of math is? sorry ):

Let V(x) = -x2 + 2x - 4 and W(x) = -~3 + 2x2 + x +, 5. Find
V(x) + W(x).
ASAP

Answers

Answer:

-x3+x2+3x+1

Step-by-step explanation:

V(x) + W(x) = -x2 + 2x - 4 + -x3 + 2x2 + x + 5= -x3+x2+3x+1

solve for x.
solve for x.
solve for x.

Answers

Answer:

[tex]x=10[/tex]

Step-by-step explanation:

A secant is a line segment that intersects a circle in two places. One property of a secant is the product of the lengths ratio. This ratio can be described as the following, let ([tex]inside[/tex]) refer to the part of the secant that is inside the circle, and ([tex]outside[/tex]) refer to the part that is outside of it. ([tex]total[/tex]) will refer to the entirety of the secant or ([tex]inside+outside[/tex]). The numbers (1) and (2) will be used as subscripts to indicate that there are two different secants.

[tex](outside_1)(total_2)=(outside_2)(total_2)[/tex]

Substitute,

[tex](outside_1)(total_2)=(outside_2)(total_2)[/tex]

[tex](outside_1)(inside_1+outisde_1)=(outside_2)(inside_2+outside_2)[/tex]

[tex](6)(6+x+5)=(7)(7+x+1)[/tex]

Simplify,

[tex](6)(6+x+5)=(7)(7+x+1)[/tex]

[tex]6(x+11)=7(x+8)[/tex]

[tex]6x+66=7x+56[/tex]

Inverse operations,

[tex]6x+66=7x+56[/tex]

[tex]66=x+56[/tex]

[tex]10=x[/tex]

The amount of grain that a shape will hold is called the surface area.

True
False

Answers

false because the grain the shape will hold is called the surface area

Answer:

false =D

Step-by-step explanation:

Pls help area geometry! I’ve got 40 steps to do in a day :(

Answers

Answer:

26 cm^2

Step-by-step explanation:

(b*h)/2 is the area formula of a triangle (use it for your other questions!)

base here is the bottom-most side, the one that is 13 degrees. the side that is 4 cm is the height.

13*4 = 52 and 52/2 = 26

Area is 26

Area is 26 I think sorry if not

Please explain, thank you

Answers

Answer:

C. 2.

Step-by-step explanation:

The graph descends from the left  so the coefficient of the leading term is negative. It is also a cubic equation with zeros of -20, about 6.5 and about 13. so we can write the equation as below.  The last 2 values can only be guessed because the x axis only shows values which are multiples of 5.

f(x) = a(x + 20)(x - 6.5)(x - 13)   where a is  a negative constant.

(This is only an approximation).

By the Remainder theorem, when the expression is divided by (x + 10):

f(-10) = -20 so we have

-20 = a (-10 + 20)(-10-6.5)(-10 - 13)

(10)(-16.5)(-23)a = -20

a = -20 / (10)(-16.5)(-23)

a = -0.0053

When  the equation is divided by (x - 10) then f(10)  is the remainder so substituting we have as the remainder:

-0.0053(10+20)(10-6.5)(10 -13)

-0.0053 * 30 * 3.5 * -3

= 1.7 approximately.

Looks like the answer is 2.

A computer vauled at $30,000 is depreciated to $0 value over a 6 year period. find the rate of change in the computer's value per year.

Answers

Answer:

$5000 per year

Step-by-step explanation:

Given data

initial value of the computer= $30000

Final value = $0

Duration= 6years

Hence the rate of change in the value per year is

=30000/6

=$5000 per year

PLEASEEEE HELLLLP MEEEE

Answers

Answer:

c. 20/21

Step-by-step explanation:

You just multiply straight

3×7 = 21

4×5 =20

21/20 <---- and it can't be reduced farther than this.

Answer:

C. ²¹⁄₂₀

Step-by-step explanation:

OKOKOK DON'T WORRY I'M HERE :)))

--

When multiplying fractions, you multiply the numerators together and then multiply the denominators together.

The numerators here are 3 and 7. Multiply those and you get 21 (7 x 3 = 21).

The denominators here are 4 and 5. Multiply those and you get 20 (4 x 5 = 20).

Then you put the newly-multiplied numerator over the newly-multiplied denominator and you get ²¹⁄₂₀.

Hope this helped!!

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